Add 1/2 (x+4)+1/4(4x-27)

Answer 1

To simplify the expression 1/2 (x+4) + 1/4(4x-27), we can start by expanding the terms within parentheses.

1/2 (x+4) = 1/2 * x + 1/2 * 4 = 1/2 * x + 2

1/4 (4x-27) = 1/4 * 4x - 1/4 * 27 = x - 27/4

Now, we can combine the two terms:

1/2 (x+4) + 1/4(4x-27) = 1/2 * x + 2 + x - 27/4

Next, we need to find a common denominator for the fractions.

The common denominator for 2 and 4 is 4, so we can rewrite 2 as 8/4:

1/2 (x+4) + 1/4(4x-27) = 1/2 * x + 8/4 + x - 27/4

Now, we can add the fractions:

1/2 * x + 8/4 + x - 27/4 = (1/2 + 8/4) * x + (1 - 27/4)

To simplify further, we can simplify the fractions:

(1/2 + 8/4) * x + (1 - 27/4) = (4/4 + 8/4) * x + (1 - 27/4) = 12/4 * x + (4/4 - 27/4) = 3 * x + (-23/4)

Therefore, the simplified expression is 3x - 23/4.